This invention relates generally to fiber-optic gyros and more specifically to the signal processing associated with fiber-optic gyros.
Fiber-optic gyros measure rate of rotation by determining the phase difference in light waves that propagate in opposite directions through a coil wound with optical fiber. Light waves that propagate through the coil in the direction of rotation take a longer time than light waves that propagate through the coil in the direction opposite to the direction of rotation. This difference in time, measured as the phase difference between counter-propagating light waves, is proportional to the angular velocity of the coil.
A typical block diagram for a fiber-optic gyro is shown in FIG. 1. A light source 2 supplies a reasonably coherent light beam to the optical-fiber interferometer 4 which causes the input light beam to be split into twvo light beams that are fed into opposite ends of an optical fiber configured as a coil. The light beams emerging from opposite ends of the optical fiber are recombined into a single output light beam that feeds into the detector 6.
The detected light intensity I (i.e. output of the detector 6) is given by ##EQU1## where I.sub.o is the peak detected light intensity and .theta.(t) is the phase difference between the two beams expressed as a function of time.
The phase difference .theta.(t) typically takes the form EQU .theta.(t)=[.PHI.(t)].sub.mod2.pi. -[.PHI.(t-.tau.)].sub.mod2.pi. +.phi..sub.S +2.pi.n (2)
where .PHI.(t) is the phase-modulation generating function and .PHI.(t).sub.mod2.pi. is the phase modulation introduced by a phase modulator at one end of the fiber-optic coil in the interferometer 4, .tau. is the propagation time through the fiber optic coil, and (.phi..sub.S +2.pi.n) is the so-called Sagnac phase resulting from the rotation of the fiber-optic coil about its axis. The integer n (called the Sagnac fringe number) is either positive or negative and the Sagnac residual phase .phi..sub.S is constrained to the range -.pi..ltoreq..phi..sub.S &lt;.pi..
The output of the detector 6 is high-pass filtered to remove the DC component, then converted to digital form by the analog-to-digital converter 8, and finally processed in the digital processor 10 to yield at the output a measure of the rate and angle of rotation of the interferometer 4. In addition, the digital processor 10 generates a phase-modulation generating function .PHI.(t), the modulo-2.pi. portion of which is converted to analog form by the digital-to-analog converter 12 and supplied to the phase modulator in the interferometer 4.
The phase-modulation generating function .PHI.(t) typically consists of a number of phase-modulation components among which are .PHI..sub.SE (t) and .PHI..sub.M (t). The phase-modulation component .PHI..sub.SE (t) is typically a stepped waveform with steps that change in height by -.phi..sub.SE at .tau. intervals where .phi..sub.SE is an estimate of .phi..sub.S. Thus, the .PHI..sub.SE (t) modulation cancels in large part .phi..sub.S. The accurate measurement of the uncancelled portion of the Sagnac residual phase .phi..sub.S is of great importance in that it is the quantity that is used in refining the estimate of the Sagnac phase and generating the .PHI..sub.SE (t) phase-modulation component.
The accurate measurement of the uncancelled portion of the Sagnac residual phase is greatly facilitated by choosing the .PHI..sub.M (t) phase-modulation component such that [.PHI..sub.M (t)-.PHI..sub.M (t-.tau.)] is equal to j.phi..sub.M where the permitted values of j are the values -1 and 1 and .phi..sub.M is a predetermined positive phase angle somewhere in the vicinity .pi./2 radians where the slope of the cosine function is greatest. This effect can be achieved, for example, by having .PHI..sub.M (t) be a square wave with amplitude .pi./2 and period 2.tau..
While it might appear that the best choice for .phi..sub.M would be .pi./2 where the slope of the cosine function is greatest, it has been shown that values between .pi./2 and .pi. provide better noise performance.
The .PHI..sub.M (t) modulation can also be a stepped function wherein the phase increases or decreases at .tau. intervals by .phi..sub.M. Under these circumstances, EQU [.PHI.(t)].sub.mod2.pi. -[.PHI.(t-.tau.)].sub.mod2.pi. =2.pi.k-.phi..sub.SE +j.phi..sub.M (3)
Substituting these expressions in equation (2), we obtain EQU .theta.=2.pi.(k+n)+j.phi..sub.M (4)
The equation above is the ideal phase difference equation, where .phi..sub.S -.phi..sub.SE =0. For fiber-optic closed-loop calculation, two control parameters are inserted into the phase difference equation with the following result: ##EQU2## The rebalance phase error .epsilon. is given by EQU .epsilon.=.phi..sub.S -.phi..sub.SE (6)
and the phase modulator scale factor error .delta./.pi. is given by ##EQU3## where .phi..sub.X is the change in light phase caused by a phase modulation step intended to produce a change of X radians. Note that if .phi..sub.x were correct and equal to X, then .delta. would be equal to zero.
The parameters .phi..sub.SE and .phi..sub.X (for a particular X) are driven by control loops to force the two demodulated signals to zero. TFhe rebalance phase demodulation equation is ##EQU4## and the scale factor demodulation equation is ##EQU5## where p.sub.kj is the probability of occurrence of each state, D.sub.kj is the scale factor demodulation polarity, I.sub.kj is the detected light intensity which may be a function of k and j, and I.sub.av is the average of I.sub.kj. The quantity I.sub.kj -I.sub.av is the amplitude of the signal that results from the high-pass filtering of the output signal from detector 6.
Fiber optic gyros generally employ broadband light sources in order to avoid polarization cross-coupling effects as the light propagates through the fiber. As a result, however, coherence is lost as non-reciprocal phase shifts between the clockwise and counter-clockwise beams are introduced. This leads to the "fringe visibility effect" whereby the interference pattern between the two beams loses contrast as the difference in optical paths increases.